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install.packages("tidyverse")

also installing the dependencies ‘DBI’, ‘dbplyr’, ‘modelr’, ‘reprex’

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trying URL 'https://cran.rstudio.com/bin/macosx/el-capitan/contrib/3.5/reprex_0.3.0.tgz'
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trying URL 'https://cran.rstudio.com/bin/macosx/el-capitan/contrib/3.5/tidyverse_1.2.1.tgz'
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The downloaded binary packages are in
    /var/folders/jb/5s85b1c570b6rhdk3p3yr6xr0000gn/T//RtmpQVYylN/downloaded_packages

library(ggplot2)
library(dplyr)
library(gridExtra)
library(magrittr)
library(RColorBrewer)
attach(Housesale)

The following objects are masked from Housesale (pos = 3):

    bathrooms, bedrooms, condition, date, floors, grade, id, isreno, lat, long, price, sqft_above,
    sqft_basement, sqft_living, sqft_living15, sqft_lot, sqft_lot15, view, waterfront, yr_built,
    yr_renovated, zipcode

The following objects are masked from Housesale (pos = 5):

    bathrooms, bedrooms, condition, date, floors, grade, id, isreno, lat, long, price, sqft_above,
    sqft_basement, sqft_living, sqft_living15, sqft_lot, sqft_lot15, view, waterfront, yr_built,
    yr_renovated, zipcode

The following objects are masked from Housesale (pos = 7):

    bathrooms, bedrooms, condition, date, floors, grade, id, isreno, lat, long, price, sqft_above,
    sqft_basement, sqft_living, sqft_living15, sqft_lot, sqft_lot15, view, waterfront, yr_built,
    yr_renovated, zipcode

The following objects are masked from Housesale (pos = 11):

    bathrooms, bedrooms, condition, date, floors, grade, id, lat, long, price, sqft_above,
    sqft_basement, sqft_living, sqft_living15, sqft_lot, sqft_lot15, view, waterfront, yr_built,
    yr_renovated, zipcode

library(readr)
library(caret)
library(corrplot)
library(caTools)
library(tidyverse)

── Attaching packages ─────────────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
✔ tibble  2.1.3     ✔ purrr   0.3.2
✔ tidyr   0.8.3     ✔ stringr 1.4.0
✔ tibble  2.1.3     ✔ forcats 0.4.0
── Conflicts ────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ gridExtra::combine() masks dplyr::combine()
✖ tidyr::extract()     masks magrittr::extract()
✖ dplyr::filter()      masks stats::filter()
✖ dplyr::lag()         masks stats::lag()
✖ purrr::lift()        masks caret::lift()
✖ purrr::set_names()   masks magrittr::set_names()

library(randomForest)

randomForest 4.6-14
Type rfNews() to see new features/changes/bug fixes.

Attaching package: ‘randomForest’

The following object is masked from ‘package:gridExtra’:

    combine

The following object is masked from ‘package:dplyr’:

    combine

The following object is masked from ‘package:ggplot2’:

    margin

## Importing data from CSV and summary
getwd()

[1] "/Users/saileshraturi/Documents/GitHub/Regression-House-Sale"

setwd("/Users/saileshraturi/Documents/GitHub/Regression-House-Sale")
Housesale = read.csv("kc_house_data.csv")
Housesale

head(Housesale)

str(Housesale)

'data.frame':   21613 obs. of  21 variables:
 $ id           : num  7.13e+09 6.41e+09 5.63e+09 2.49e+09 1.95e+09 ...
 $ date         : Factor w/ 372 levels "20140502T000000",..: 165 221 291 221 284 11 57 252 340 306 ...
 $ price        : num  221900 538000 180000 604000 510000 ...
 $ bedrooms     : int  3 3 2 4 3 4 3 3 3 3 ...
 $ bathrooms    : num  1 2.25 1 3 2 4.5 2.25 1.5 1 2.5 ...
 $ sqft_living  : int  1180 2570 770 1960 1680 5420 1715 1060 1780 1890 ...
 $ sqft_lot     : int  5650 7242 10000 5000 8080 101930 6819 9711 7470 6560 ...
 $ floors       : num  1 2 1 1 1 1 2 1 1 2 ...
 $ waterfront   : int  0 0 0 0 0 0 0 0 0 0 ...
 $ view         : int  0 0 0 0 0 0 0 0 0 0 ...
 $ condition    : int  3 3 3 5 3 3 3 3 3 3 ...
 $ grade        : int  7 7 6 7 8 11 7 7 7 7 ...
 $ sqft_above   : int  1180 2170 770 1050 1680 3890 1715 1060 1050 1890 ...
 $ sqft_basement: int  0 400 0 910 0 1530 0 0 730 0 ...
 $ yr_built     : int  1955 1951 1933 1965 1987 2001 1995 1963 1960 2003 ...
 $ yr_renovated : int  0 1991 0 0 0 0 0 0 0 0 ...
 $ zipcode      : int  98178 98125 98028 98136 98074 98053 98003 98198 98146 98038 ...
 $ lat          : num  47.5 47.7 47.7 47.5 47.6 ...
 $ long         : num  -122 -122 -122 -122 -122 ...
 $ sqft_living15: int  1340 1690 2720 1360 1800 4760 2238 1650 1780 2390 ...
 $ sqft_lot15   : int  5650 7639 8062 5000 7503 101930 6819 9711 8113 7570 ...

summary(Housesale)

       id                         date           price            bedrooms        bathrooms      sqft_living   
 Min.   :1.000e+06   20140623T000000:  142   Min.   :  75000   Min.   : 0.000   Min.   :0.000   Min.   :  290  
 1st Qu.:2.123e+09   20140625T000000:  131   1st Qu.: 321950   1st Qu.: 3.000   1st Qu.:1.750   1st Qu.: 1427  
 Median :3.905e+09   20140626T000000:  131   Median : 450000   Median : 3.000   Median :2.250   Median : 1910  
 Mean   :4.580e+09   20140708T000000:  127   Mean   : 540088   Mean   : 3.371   Mean   :2.115   Mean   : 2080  
 3rd Qu.:7.309e+09   20150427T000000:  126   3rd Qu.: 645000   3rd Qu.: 4.000   3rd Qu.:2.500   3rd Qu.: 2550  
 Max.   :9.900e+09   20150325T000000:  123   Max.   :7700000   Max.   :33.000   Max.   :8.000   Max.   :13540  
                     (Other)        :20833                                                                     
    sqft_lot           floors        waterfront            view          condition         grade       
 Min.   :    520   Min.   :1.000   Min.   :0.000000   Min.   :0.0000   Min.   :1.000   Min.   : 1.000  
 1st Qu.:   5040   1st Qu.:1.000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:3.000   1st Qu.: 7.000  
 Median :   7618   Median :1.500   Median :0.000000   Median :0.0000   Median :3.000   Median : 7.000  
 Mean   :  15107   Mean   :1.494   Mean   :0.007542   Mean   :0.2343   Mean   :3.409   Mean   : 7.657  
 3rd Qu.:  10688   3rd Qu.:2.000   3rd Qu.:0.000000   3rd Qu.:0.0000   3rd Qu.:4.000   3rd Qu.: 8.000  
 Max.   :1651359   Max.   :3.500   Max.   :1.000000   Max.   :4.0000   Max.   :5.000   Max.   :13.000  
                                                                                                       
   sqft_above   sqft_basement       yr_built     yr_renovated       zipcode           lat       
 Min.   : 290   Min.   :   0.0   Min.   :1900   Min.   :   0.0   Min.   :98001   Min.   :47.16  
 1st Qu.:1190   1st Qu.:   0.0   1st Qu.:1951   1st Qu.:   0.0   1st Qu.:98033   1st Qu.:47.47  
 Median :1560   Median :   0.0   Median :1975   Median :   0.0   Median :98065   Median :47.57  
 Mean   :1788   Mean   : 291.5   Mean   :1971   Mean   :  84.4   Mean   :98078   Mean   :47.56  
 3rd Qu.:2210   3rd Qu.: 560.0   3rd Qu.:1997   3rd Qu.:   0.0   3rd Qu.:98118   3rd Qu.:47.68  
 Max.   :9410   Max.   :4820.0   Max.   :2015   Max.   :2015.0   Max.   :98199   Max.   :47.78  
                                                                                                
      long        sqft_living15    sqft_lot15    
 Min.   :-122.5   Min.   : 399   Min.   :   651  
 1st Qu.:-122.3   1st Qu.:1490   1st Qu.:  5100  
 Median :-122.2   Median :1840   Median :  7620  
 Mean   :-122.2   Mean   :1987   Mean   : 12768  
 3rd Qu.:-122.1   3rd Qu.:2360   3rd Qu.: 10083  
 Max.   :-121.3   Max.   :6210   Max.   :871200  
                                                 

log_sqftliving = log10(sqft_living)
Housesale = Housesale %>% mutate(log_price = log10(price))
x = min(sqft_living)
y = max(sqft_living)
z = (y-x)

#taking anitlog
l1 = exp(2.9)
l1

[1] 18.17415

l2 = exp(3.6)
l2

[1] 36.59823

#Plot for Price
g1 = ggplot(Housesale, aes(x = log_price)) + geom_histogram(fill = "red", binwidth = .10)
#Plot for sqftliving
g2 = ggplot(Housesale, aes(x = log_sqftliving)) + geom_histogram(fill = "blue", binwidth = .20)
 
# grid.arrange(g1,g2,nrow = 1,ncol = 2)

 #House Price : Plot reflect the most of the prices of house is lie between 5.4 to 6 million.
 #Sqftliving :  Most of houses have  sqft living between 1800 to 3600 sqft.
 

 #plot for bathroom
 
 ggplot(Housesale, aes(x = bathrooms)) + geom_histogram(fill = "tomato", binwidth = 0.5) + scale_x_continuous(limits = c(1,8))

x = max(bathrooms)
y = min(bathrooms)
z = mad(bathrooms)

#House Price vs size

#jitter used to reduce overlapping
g3 = ggplot(Housesale, aes(x = log_sqftliving, y = log_price)) +  geom_jitter(alpha = 0.5, size = 2, color = "brown") + stat_smooth(method = "lm", se = F, span = 0.7) + labs("title = sqftliving vs Price")

#HousePrice vs Bedroom

mycolors = c(brewer.pal(name = "Dark2", n=8), brewer.pal(name="Paired", n=6))
#Housesale = Housesale %>% filter(bedrooms < 30)
#Housesale
g4 = ggplot(Housesale, aes(x = bedrooms, y = log_price, col = bedrooms)) + geom_point(alpha = 0.5, size = 2) + geom_smooth(method = "lm",se = F) + scale_color_gradientn(colors = mycolors)

grid.arrange(g3,g4,nrow = 1, ncol = 2)

#ggplot(aes(Housesale,x=bedrooms,y=log_price))+
#geom_point(alpha=0.5,size=2)+
#geom_smooth(method="lm",se=F)+
#labs("title=Bedrooms vs Price")+scale_color_gradientn(colors=mycolors)+theme(legend.position="none")

 g5 = ggplot(Housesale, aes(x = sqft_basement, y = log_price)) + geom_point( col = "green", alpha = 0.5) + stat_smooth(method = "lm", se = F, alpha = 0.6, size = 0.5)

g6 = ggplot(Housesale, aes(x = yr_built, y = log_price)) + geom_jitter(col = "blue", alpha = 0.5) + geom_smooth(method = "auto", se = T)

grid.arrange(g5,g6,nrow = 1, ncol = 2)

table(condition)

condition
    1     2     3     4     5 
   30   172 14031  5679  1701 

Housesale %>% group_by(factor(condition)) %>% summarise(mean_price = mean(log_price), sd = sd(log_price), count = n())

# Distribution of Houseprice according to condition of house

ggplot(Housesale, aes(x = factor(condition), y = log_price, fill = factor(condition))) + geom_boxplot()

# Relationship between, size, price and condition
ggplot(Housesale, aes(x = log_sqftliving, y = log_price, color = factor(condition))) + geom_point(alpha = 0.5) +  geom_smooth(method = "lm", se = F, color = "Black") + facet_wrap(~condition) 

#grid.arrange(g7, g8, nrow = 1, ncol = 2)

table(floors)
Housesale %>% group_by(flr = factor(floors)) %>% summarise(floor_cnt = n()) %>%
ggplot(aes(x = flr,floor_cnt, fill = flr)) + geom_bar(stat = "identity")

#hist(floors)

ggplot(Housesale, aes(x = factor(floors), y = (log_price),fill = factor(floors))) + geom_boxplot()

#ggplot(Housesale, aes(x = yr_built, y = log_price)) + geom_point()
#+ 
#Houses bulit yearly

Housesale %>% ggplot(aes(x = yr_built)) + geom_histogram(binwidth = 5, fill = rainbow(1), alpha = 0.5) + scale_x_continuous(limits = c(1900,2016))

# House built year wise vs size of house(sqft)
options(repr.plot.width = 10, repr.plot.height = 6)
ggplot(Housesale, aes(x = factor(yr_built), y = log_sqftliving, fill = factor(yr_built))) + geom_boxplot() + theme(legend.position = "none") 

ggplot(Housesale, aes(x=yr_built, y = log_sqftliving, color = "green")) + geom_jitter(alpha =0.5, size = 0.5) + stat_smooth(method = "auto", color = "black")

# trend of increase in sqft living 1950 onwards till 1990

#House View

table(Housesale$waterfront)

Housesale$houseview = ifelse(waterfront ==1,TRUE,FALSE)
#ggplot(Housesale, aes(x = houseview, y = log_price, fill = factor(waterfront))) + geom_boxplot()
# Most of the houses doesnot have waterfront while houses with waterfront are more expensive

Housesale %>% group_by(houseview) %>% summarise(meanprice = mean(log_price),housecount = n() )

ggplot(Housesale,aes( x = log_sqftliving, y= log_price, col = houseview)) + geom_point(alpha = 0.5) + geom_smooth(method = "lm" ,size =0.5, color = "black") + scale_color_manual(values = rainbow(n=12)) +facet_wrap(~houseview)
# sold houses which have waterfront are expensive and high sqftliving but less in number

table(grade)

#grade vs price

#ggplot(Housesale, aes(x = factor(grade), y = log_price, fill = factor(grade))) + geom_boxplot(alpha = 0.5)

# grade vs sqftliving vs price

ggplot(Housesale, aes(x = log_sqftliving, y = log_price, color = factor(grade))) + geom_point(alpha = 0.5) + facet_wrap(~grade) + geom_smooth(method = "lm", color = "black") + scale_color_manual(values = rainbow(n=12)) + theme(legend.position = "none")

# Renovate year

table(Housesale$yr_renovated)

Housesale$isreno = ifelse(yr_renovated == 0, FALSE, TRUE)
table(Housesale$isreno)

# histogram of yr renovated
ggplot(Housesale, aes(yr_renovated)) + geom_histogram(alpha = 0.5,binwidth = 1, fill = rainbow(1)) + scale_x_continuous(limits = c(1900,2016))

#ggplot(Housesale, aes(x = factor(yr_renovated), y= log_price, fill = factor(yr_renovated))) + geom_boxplot()

# year built vs price vs renovate
ggplot(Housesale, aes(x = yr_built, y = log_price, col = yr_renovated)) + geom_jitter(alpha = 0.5)

#Renovate year vs year built
ggplot(Housesale, aes(x = yr_built, y = yr_renovated, color = isreno)) + geom_jitter(alpha = 0.5) + facet_wrap(~isreno)

#splitting the data into train and test subset
set.seed(0512)
sample = sample.split(Housesale, SplitRatio = .70)
trainhs = subset(Housesale, sample == TRUE)
tesths = subset(Housesale, sample == FALSE)
nrow(Housesale)

[1] 21613

ncol(Housesale)

[1] 22

nrow(trainhs)

[1] 14736

nrow(tesths)

[1] 6877

# variable significance and checking correlation

corr =  cor(Housesale[,3:21])
corrplot(corr)

NA
NA
NA

# model creation using linear regression(parameters on basis of correleation matrix)

modellm1 = lm(log(price) ~ bedrooms + bathrooms + sqft_living + waterfront + view + condition + grade + yr_built + yr_renovated + zipcode  + lat + sqft_living15 + sqft_lot15   , data = trainhs)

summary(modellm1)
#plot(modellm1)

# model creation using linear regression or training model( all parameters)
modellm2 = lm(log(price) ~ ., data = trainhs[,3:22])
summary(modellm2)
#plot(modellm2)

# model creation using linear regression using cross-validation technique(partitioning dataset into random partition - train and test(number of folds), average of accuracy metrics for all folds taken to come across how training model will perform on unknown test dataset)
#modellm3 = train(log(price) ~ .,data = trainhs[,3:22], method = "lm", trControl = trainControl(method = "cv",number = 10, savePredictions = TRUE))
install.packages("ggfortify")
modellm3 = train(price ~ .,data = Housesale, method = "lm", trControl = trainControl(method = "cv",number = 5, verboseIter = TRUE))
summary(modellm3)
library(ggfortify)
autoplot(modellm3,ncol = 2)

# model creation using linear regression using cross-validation technique(partitioning dataset into random partition - train and test(number of folds), average of accuracy metrics for all folds taken to come across how training model will perform on unknown test dataset)
modellm6 = train(log(price) ~  bedrooms + bathrooms + sqft_living + waterfront + view + condition + grade + yr_built + yr_renovated  + lat + sqft_living15 + sqft_lot15 + I(bedrooms^2)  + I(sqft_living^2) + I(view^2) + I(grade^2) + I(yr_built^2) + I(yr_renovated^2)  + I(lat^2) + I(sqft_living15^2)+ I(sqft_lot15^2),data = trainhs[,3:22], method = "lm", trControl = trainControl(method = "cv",number = 10, savePredictions = TRUE))
summary(modellm6)
#parametergrid <- expand.grid(c(5,6,7,8))
#summary(modellm3)

#checking residuals plot for each parameter
g1 = ggplot(trainhs, aes(bathrooms, residuals(modellm1))) + geom_point() + geom_smooth()
g2 = ggplot(trainhs, aes(sqft_living, residuals(modellm1))) + geom_point() + geom_smooth()
g3 = ggplot(trainhs, aes(view, residuals(modellm1))) + geom_point() + geom_smooth()
g4 = ggplot(trainhs, aes(grade, residuals(modellm1))) + geom_point() + geom_smooth()
g5 = ggplot(trainhs, aes(yr_built, residuals(modellm1))) + geom_point() + geom_smooth()
g6 =ggplot(trainhs, aes(sqft_living15, residuals(modellm1))) + geom_point() + geom_smooth()
g7 = ggplot(trainhs, aes(bedrooms, residuals(modellm1))) + geom_point() + geom_smooth()
g8 = ggplot(trainhs, aes(waterfront, residuals(modellm1))) + geom_point() + geom_smooth()
g9 = ggplot(trainhs, aes(lat, residuals(modellm1))) + geom_point() + geom_smooth()
g10 =ggplot(trainhs, aes(sqft_lot15, residuals(modellm1))) + geom_point() + geom_smooth()
g11 =ggplot(trainhs, aes(condition, residuals(modellm1))) + geom_point() + geom_smooth()
g12 =ggplot(trainhs, aes(yr_renovated, residuals(modellm1))) + geom_point() + geom_smooth()
g13 =ggplot(trainhs, aes(zipcode, residuals(modellm1))) + geom_point() + geom_smooth()

grid.arrange(g1,g2,g3,g4, nrow = 1, ncol = 4)
grid.arrange(g5,g6,g7,g8, nrow = 1, ncol = 4)
grid.arrange(g9,g10,g11,g12,g13, nrow = 1, ncol = 5)

#model creation using nonlinearlity of parameters based on residuals plot
#modellm4 = lm(log(price) ~  bedrooms + bathrooms + sqft_living + waterfront + view + condition + grade + yr_built + yr_renovated + zipcode  + lat + sqft_living15 + sqft_lot15 + I(bedrooms^2) + I(bathrooms^2) + I(sqft_living^2)+ I(waterfront^2)  + I(view^2) + I(condition^2) + I(grade^2) + I(yr_built^2) + I(yr_renovated^2)  +I(zipcode^2)  + I(lat^2) + I(sqft_living15^2)+ I(sqft_lot15^2) , data = trainhs)
#summary(modellm4)
#plot(modellm4)
modellm4 = lm(log(price) ~  bedrooms + bathrooms + sqft_living + waterfront + view + condition + grade + yr_built + yr_renovated + zipcode  + lat + sqft_living15 + sqft_lot15 + I(bedrooms^2) + I(bathrooms^2) + I(sqft_living^2)  + I(grade^2) + I(yr_built^2) + I(yr_renovated^2)  +I(zipcode^2)  + I(lat^2) + I(sqft_living15^2)+ I(sqft_lot15^2) , data = trainhs)
summary(modellm4)

#model creation after removing less significant parameters identified in modellm4
#modellm5 = update(modellm4, ~.-zipcode-I(bathrooms^2)-I(waterfront^2)-I(condition^2)-I(zipcode^2))
modellm5 = lm(log(price) ~  bedrooms + bathrooms + sqft_living + waterfront + view + condition + grade + yr_built + yr_renovated  + lat + sqft_living15 + sqft_lot15 + I(bedrooms^2)  + I(sqft_living^2) + I(view^2) + I(grade^2) + I(yr_built^2) + I(yr_renovated^2)  + I(lat^2) + I(sqft_living15^2)+ I(sqft_lot15^2) , data = trainhs)
summary(modellm5)

Call:
lm(formula = log(price) ~ bedrooms + bathrooms + sqft_living + 
    waterfront + view + condition + grade + yr_built + yr_renovated + 
    lat + sqft_living15 + sqft_lot15 + I(bedrooms^2) + I(sqft_living^2) + 
    I(view^2) + I(grade^2) + I(yr_built^2) + I(yr_renovated^2) + 
    I(lat^2) + I(sqft_living15^2) + I(sqft_lot15^2), data = trainhs)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.25879 -0.14747 -0.00418  0.14024  1.14221 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)        -7.067e+03  2.283e+02 -30.948  < 2e-16 ***
bedrooms           -2.185e-02  4.213e-03  -5.187 2.16e-07 ***
bathrooms           5.025e-02  4.649e-03  10.809  < 2e-16 ***
sqft_living         2.146e-04  9.006e-06  23.835  < 2e-16 ***
waterfront          4.151e-01  2.783e-02  14.918  < 2e-16 ***
view                9.124e-02  9.776e-03   9.333  < 2e-16 ***
condition           7.457e-02  3.418e-03  21.817  < 2e-16 ***
grade               1.809e-01  1.776e-02  10.188  < 2e-16 ***
yr_built           -2.041e-01  9.199e-03 -22.188  < 2e-16 ***
yr_renovated       -5.557e-03  6.422e-04  -8.653  < 2e-16 ***
lat                 3.050e+02  9.574e+00  31.857  < 2e-16 ***
sqft_living15       2.564e-04  1.569e-05  16.339  < 2e-16 ***
sqft_lot15          8.378e-07  1.205e-07   6.955 3.68e-12 ***
I(bedrooms^2)       8.598e-04  2.902e-04   2.962 0.003057 ** 
I(sqft_living^2)   -9.959e-09  1.247e-09  -7.985 1.51e-15 ***
I(view^2)          -9.144e-03  3.168e-03  -2.886 0.003904 ** 
I(grade^2)         -1.508e-03  1.107e-03  -1.363 0.172994    
I(yr_built^2)       5.134e-05  2.347e-06  21.880  < 2e-16 ***
I(yr_renovated^2)   2.806e-06  3.218e-07   8.720  < 2e-16 ***
I(lat^2)           -3.194e+00  1.007e-01 -31.714  < 2e-16 ***
I(sqft_living15^2) -3.648e-08  3.193e-09 -11.426  < 2e-16 ***
I(sqft_lot15^2)    -1.053e-12  2.992e-13  -3.520 0.000433 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.239 on 14714 degrees of freedom
Multiple R-squared:  0.7926,    Adjusted R-squared:  0.7923 
F-statistic:  2677 on 21 and 14714 DF,  p-value: < 2.2e-16

plot(modellm5)

NA

# rmse for regression model

testmodel = predict(modellm7, tesths[,3:21])
plot(exp(testmodel) ~ tesths$price)
#plot(testmodel ~ tesths$price)
abline(a = 0, b = 1)

res1 =  exp(testmodel) - tesths$price
#res1 =  testmodel - tesths$price
#rmse <- sqrt(sum((exp(testmodel) - tesths$price)^2)/length(tesths$price))
rmse = sqrt(mean(res1^2))
rmse

[1] 199403.9

#trying random forest model
modelrf  = randomForest(price ~ ., trainhs[,3:21],mtry = 6, importance = TRUE)
summary(modelrf)
importance(modelrf)
varImpPlot(modelrf,type = 2)
para = sqft_living+grade+lat+sqft_living15+sqft_above+long+bathrooms+yr_built + view

modellm7 = lm(log(price) ~ sqft_living + grade + lat + sqft_living15 + sqft_above + long + bathrooms + yr_built + view, data = trainhs[,3:21])
summary(modellm7)

Call:
lm(formula = log(price) ~ sqft_living + grade + lat + sqft_living15 + 
    sqft_above + long + bathrooms + yr_built + view, data = trainhs[, 
    3:21])

Residuals:
     Min       1Q   Median       3Q      Max 
-1.79935 -0.16215  0.00189  0.16113  1.24437 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -5.151e+01  2.327e+00 -22.133  < 2e-16 ***
sqft_living    1.274e-04  6.197e-06  20.553  < 2e-16 ***
grade          1.681e-01  3.300e-03  50.925  < 2e-16 ***
lat            1.333e+00  1.596e-02  83.499  < 2e-16 ***
sqft_living15  9.225e-05  5.284e-06  17.459  < 2e-16 ***
sqft_above     1.332e-05  6.033e-06   2.208  0.02729 *  
long          -5.337e-02  1.777e-02  -3.003  0.00268 ** 
bathrooms      8.879e-02  4.723e-03  18.800  < 2e-16 ***
yr_built      -3.712e-03  9.879e-05 -37.572  < 2e-16 ***
view           7.622e-02  3.037e-03  25.095  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2587 on 14726 degrees of freedom
Multiple R-squared:  0.7569,    Adjusted R-squared:  0.7567 
F-statistic:  5093 on 9 and 14726 DF,  p-value: < 2.2e-16

#rmse for random forest model
testmodel_rf = predict(modelrf, tesths)
#p1 = plot(tesths$price ~ exp(testmodel))
#abline(a =0, b =1)
#p2 = plot(tesths$price ~ testmodel_rf)
#abline(a =0, b =1)

#grid.arrange(p1,p2, nrow = 1, ncol = 2)
res1 =  testmodel_rf - tesths$price
rmse = sqrt(mean(res1^2))
rmse

[1] 135938.7